Reduction and relative equilibria for the two-body problem on spaces of constant curvature
Sign Up to like & getrecommendations! Published in 2018 at "Celestial Mechanics and Dynamical Astronomy"
DOI: 10.1007/s10569-018-9835-7
Abstract: We consider the two-body problem on surfaces of constant nonzero curvature and classify the relative equilibria and their stability. On the hyperbolic plane, for each $$q>0$$q>0 we show there are two relative equilibria where the… read more here.
Keywords: equilibria; relative equilibria; two body; body problem ... See more keywords
Spatial Relative Equilibria and Periodic Solutions of the Coulomb $$(n+1)$$-Body Problem
Sign Up to like & getrecommendations! Published in 2021 at "Qualitative Theory of Dynamical Systems"
DOI: 10.1007/s12346-021-00532-3
Abstract: We study a classical model for the atom that considers the movement of n charged particles of charge −1 (electrons) interacting with a fixed nucleus of charge μ > 0. We show that two global… read more here.
Keywords: equilibria periodic; periodic solutions; relative equilibrium; relative equilibria ... See more keywords
Localization of real algebraic hypersurfaces with applications to the enumeration of the classes of relative equilibria of a (5 + 1)-body problem
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2019.123813
Abstract: Abstract We extend classical results on the localization of zeros of real univariate polynomials to the localization of zero sets of real multivariate polynomials P, more precisely, of real algebraic hypersurfaces (assuming 0 is a… read more here.
Keywords: algebraic hypersurfaces; real algebraic; equilibria body; relative equilibria ... See more keywords
Dynamics of a Circular Foil and Two Pairs of Point Vortices: New Relative Equilibria and a Generalization of Helmholtz Leapfrogging
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DOI: 10.3390/sym15030698
Abstract: In this paper, we study the plane-parallel motion of a circular foil interacting with two vortex pairs in an infinite volume of an ideal fluid. We assumed that the circulation of the velocity of the… read more here.
Keywords: new relative; circular foil; helmholtz leapfrogging; relative equilibria ... See more keywords
Euler-type relative equilibria in spaces of constant curvature and their stability
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DOI: 10.4153/cjm-2017-002-7
Abstract: We consider three point positive masses moving on S and H. An Eulerianrelative equilibrium, is a relative equilibriumwhere the threemasses are on the same geodesic, in this paper we analyze the spectral stability of these… read more here.
Keywords: case; relative equilibria; euler type; spectrally stable ... See more keywords